Method of controlling and correcting an asymmetric waveform

ABSTRACT

Disclosed is a method of controlling an asymmetric waveform generated as a combination of two sinusoidal waves having a frequency that differs by a factor of two. A method according to the instant invention includes a step of sampling a generated asymmetric waveform to obtain a set of data points, the set of data points being indicative of the generated asymmetric waveform. The sampled data points are arranged in an order according to magnitude, and then compared to template data relating to a desired asymmetric waveform. In dependence upon the comparison, a correction to the generated asymmetric waveform is determined.

This application claims the benefit of U.S. Provisional Application No.60/413,162, filed Sep. 25, 2002.

FIELD OF THE INVENTION

The instant invention relates generally to high field asymmetricwaveform ion mobility spectrometry (FAIMS), more particularly theinstant invention relates to a method of optimizing asymmetric waveformgenerator LC tuning electronics.

BACKGROUND OF THE INVENTION

High sensitivity and amenability to miniaturization for field-portableapplications have helped to make ion mobility spectrometry (IMS) animportant technique for the detection of many compounds, includingnarcotics, explosives, and chemical warfare agents as described, forexample, by G. Eiceman and Z. Karpas in their book entitled “IonMobility Spectrometry” (CRC, Boca Raton, 1994). In IMS, gas-phase ionmobilities are determined using a drift tube with a constant electricfield. Ions are separated in the drift tube on the basis of differencesin their drift velocities. At low electric field strength, for example200 V/cm, the drift velocity of an ion is proportional to the appliedelectric field strength, and the mobility, K, which is determined fromexperimentation, is independent of the applied electric field.Additionally, in IMS the ions travel through a bath gas that is atsufficiently high pressure that the ions rapidly reach constant velocitywhen driven by the force of an electric field that is constant both intime and location. This is to be clearly distinguished from thosetechniques, most of which are related to mass spectrometry, in which thegas pressure is sufficiently low that, if under the influence of aconstant electric field, the ions continue to accelerate.

E. A. Mason and E. W. McDaniel in their book entitled “TransportProperties of Ions in Gases” (Wiley, New York, 1988) teach that at highelectric field strength, for instance fields stronger than approximately5,000 V/cm, the ion drift velocity is no longer directly proportional tothe applied electric field, and K is better represented by K_(H), anon-constant high field mobility term. The dependence of K_(H) on theapplied electric field has been the basis for the development of highfield asymmetric waveform ion mobility spectrometry (FAIMS). Ions areseparated in FAIMS on the basis of a difference in the mobility of anion at high field strength, K_(H), relative to the mobility of the ionat low field strength, K. In other words, the ions are separated due tothe compound dependent behavior of K_(H) as a function of the appliedelectric field strength.

In general, a device for separating ions according to the FAIMSprinciple has an analyzer region that is defined by a space betweenfirst and second spaced-apart electrodes. The first electrode ismaintained at a selected dc voltage, often at ground potential, whilethe second electrode has an asymmetric waveform V(t) applied to it. Theasymmetric waveform V(t) is composed of a repeating pattern including ahigh voltage component, V_(H), lasting for a short period of time t_(H)and a lower voltage component, V_(L), of opposite polarity, lasting alonger period of time t_(L). The waveform is synthesized such that theintegrated voltage-time product, and thus the field-time product,applied to the second electrode during each complete cycle of thewaveform is zero, for instance V_(H)t_(H)+V_(L) t_(L)=0; for example+2000 V for 10 μs followed by −1000 V for 20 μs. The peak voltage duringthe shorter, high voltage portion of the waveform is called the“dispersion voltage” or DV, which is identically referred to as theapplied asymmetric waveform voltage.

Generally, the ions that are to be separated are entrained in a streamof gas flowing through the FAIMS analyzer region, for example between apair of horizontally oriented, spaced-apart electrodes. Accordingly, thenet motion of an ion within the analyzer region is the sum of ahorizontal x-axis component due to the stream of gas and a transversey-axis component due to the applied electric field. During the highvoltage portion of the waveform, an ion moves with a y-axis velocitycomponent given by v_(H)=K_(H)E_(H), where E_(H) is the applied field,and K_(H) is the high field ion mobility under operating electric field,pressure and temperature conditions. The distance traveled by the ionduring the high voltage portion of the waveform is given byd_(H)=v_(H)t_(H)=K_(H)E_(H)t_(H), where t_(H) is the time period of theapplied high voltage. During the longer duration, opposite polarity, lowvoltage portion of the asymmetric waveform, the y-axis velocitycomponent of the ion is v_(L)=KE_(L), where K is the low field ionmobility under operating pressure and temperature conditions. Thedistance traveled is d_(L)=v_(L)t_(L)=KE_(L)t_(L). Since the asymmetricwaveform ensures that (V_(H) t_(H))+(V_(L) t_(L))=0, the field-timeproducts E_(H)t_(H) and E_(L)t_(L) are equal in magnitude. Thus, ifK_(H) and K are identical, d_(H) and d_(L) are equal, and the ion isreturned to its original position along the y-axis during the negativecycle of the waveform. If at E_(H) the mobility K_(H)>K, the ionexperiences a net displacement from its original position relative tothe y-axis. For example, if a positive ion travels farther during thepositive portion of the waveform, for instance d_(H)>d_(L), then the ionmigrates away from the second electrode and eventually will beneutralized at the first electrode.

In order to reverse the transverse drift of the positive ion in theabove example, a constant negative dc voltage is applied to the secondelectrode. The difference between the dc voltage that is applied to thefirst electrode and the dc voltage that is applied to the secondelectrode is called the “compensation voltage” (CV). The CV prevents theion from migrating toward either the second or the first electrode. Ifions derived from two compounds respond differently to the applied highstrength electric fields, the ratio of K_(H) to K may be different foreach compound. Consequently, the magnitude of the CV that is necessaryto prevent the drift of the ion toward either electrode is alsodifferent for each compound. Thus, when a mixture including severalspecies of ions, each with a unique K_(H)/K ratio, is being analyzed byFAIMS, only one species of ion is selectively transmitted to a detectorfor a given combination of CV and DV. In one type of FAIMS experiment,the applied CV is scanned with time, for instance the CV is slowlyramped or optionally the CV is stepped from one voltage to a nextvoltage, and a resulting intensity of transmitted ions is measured. Inthis way a CV spectrum showing the total ion current as a function ofCV, is obtained.

In FAIMS, the optimum asymmetric waveform voltage for obtaining themaximum possible ion detection sensitivity on a per cycle basis takesthe shape of an asymmetric square wave with a zero time-averaged value.In practice this asymmetric square waveform is difficult to produce andapply to the FAIMS electrodes because of electrical power consumptionconsiderations. For example, without a tuned circuit the power P whichwould be required to drive a capacitive load of capacitance C, atfrequency f, with a peak voltage V, is 2πV²fC. Accordingly, if a squarewave at 750 kHz, 4000 V peak voltage is applied to a 20 picofarad load,the power consumption will be 240 Watts. If, on the other hand, awaveform is applied via a tuned circuit, the power consumption isreduced to P(cos Θ) where Θ is the angle between the current and thevoltage applied to the capacitive load. This power consumptionapproaches zero if the current and voltage are out of phase by 90degrees, as they would be in a perfectly tuned LC circuit.

Since a tuned circuit cannot provide a square wave, an approximation ofa square wave is taken as the first terms of a Fourier series expansion.One approach is to use:V(t)=⅔D sin(ωt)+⅓D sin(2ωt−π/2)  (1)Where V(t) is the asymmetric waveform voltage as a function of time, Dis the peak voltage (defined as dispersion voltage DV), ω is thewaveform frequency in radians/sec. The first term is a sinusoidal waveat frequency ω, and the second term is a sinusoidal wave at double thefrequency of the first sinusoidal wave, 2ω. The second term could alsobe represented as a cosine, without the phase shift of π/2.

In practice, both the optimization of the LC tuning and maintenance ofthe exact amplitude of the first and second applied sinusoidal waves andthe phase angle between the two waves is required to achieve long term,stable operation of a FAIMS system powered by such an asymmetricwaveform generator. Accordingly, feedback control is required to ensurethat the output signal is stable and that the correct waveform shape ismaintained.

In U.S. Pat. No. 5,801,379, which was issued on Sep. 1, 1998, Kouznetsovteaches a high voltage waveform generator having separate phasecorrection and amplitude correction circuits. This system usesadditional hardware components in the separate phase correction andamplitude correction circuits, thereby increasing complexity andincreasing the cost of manufacturing and testing the devices.Furthermore, this system cannot be implemented into control software,making it difficult to vary certain parameters.

It is an object of the instant invention to provide a method ofoptimizing asymmetric waveform generator LC tuning electronics thatovercomes the limitations of the prior art.

SUMMARY OF THE INVENTION

In accordance with an aspect of the instant invention there is provideda method of controlling an asymmetric waveform generated as acombination of two sinusoidal waves having a frequency that differs by afactor of two, the method comprising the steps of: sampling thegenerated asymmetric waveform to obtain a set of data points that isindicative of the generated asymmetric waveform; arranging the sampleddata points in an order according to magnitude; comparing the arrangedsampled data points to template data relating to a desired asymmetricwaveform; and, in dependence upon the comparison, determining acorrection to the generated asymmetric waveform.

In accordance with another aspect of the instant invention there isprovided a method of controlling an asymmetric waveform generated as acombination of two sinusoidal waves having a frequency that differs by afactor of two, the method comprising the steps of: obtaining a set ofdata points that is indicative of the generated asymmetric waveform;arranging the data points in an order according to magnitude; obtainingtemplate data including a set of data points relating to a desiredasymmetric waveform; comparing values of data points within apredetermined range of the arranged data points to values of data pointswithin a corresponding predetermined range of the template data; and, independence upon the comparison, adjusting at least one of a phase angledifference between the two sinusoidal waves and an amplitude of at leastone of the two sinusoidal waves.

In accordance with yet another aspect of the instant invention there isprovided a storage medium encoded with machine-readable computer programcode for controlling an asymmetric waveform generated as a combinationof two sinusoidal waves having a frequency that differs by a factor oftwo, the storage medium including instructions for: obtaining a set ofdata points that is indicative of the generated asymmetric waveform;arranging the data points in an order according to magnitude; obtainingtemplate data including a set of data points relating to a desiredasymmetric waveform; comparing values of data points within apredetermined range of the arranged data points to values of data pointswithin a corresponding predetermined range of the template data; and, independence upon the comparison, adjusting at least one of a phase angledifference between the two sinusoidal waves and an amplitude of at leastone of the two sinusoidal waves.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention will now be described inconjunction with the following drawings, in which similar referencenumerals designate similar items:

FIG. 1 shows a plurality of cycles of an asymmetric waveform that isformed as a combination of first and second sinusoidal waves offrequency ω and 2ω, respectively;

FIG. 2 shows a distribution of data points from one cycle of thewaveform shown in FIG. 1;

FIG. 3 shows an analysis of the magnitudes of changes and wheredeviations appear in the data of FIG. 2 as a result of three types ofdeviation from ideality;

FIG. 4 a shows the data of FIG. 3 on an expanded vertical scale;

FIG. 4 b shows a relative error plot corresponding to a waveform with aphase shift error;

FIG. 4 c shows a relative error plot corresponding to a waveform with anerror in the relative amplitude of the component sinusoidal waves;

FIG. 4 d shows a relative error plot corresponding to a waveform with anerror in the sum of the amplitudes of the component sinusoidal waves;

FIG. 5 shows a simplified flow diagram of a method of optimizingasymmetric waveform generator LC tuning electronics according to anembodiment of the instant invention;

FIG. 6 shows a simplified flow diagram of a method of optimizingasymmetric waveform generator LC tuning electronics according to anotherembodiment of the instant invention;

FIG. 7 shows a simplified flow diagram of a method of adjusting thedifferent waveform parameters;

FIG. 8 shows a trace of an asymmetric waveform having an A+B type error,a phase angle error and an A/B type error superimposed thereon;

FIG. 9 shows a trace of an asymmetric waveform having a phase angleerror and an A/B type error superimposed thereon; and,

FIG. 10 shows a simplified flow diagram of another method of adjustingthe different waveform parameters.

DETAILED DESCRIPTION OF THE DRAWINGS

The following description is presented to enable a person skilled in theart to make and use the invention, and is provided in the context of aparticular application and its requirements. Various modifications tothe disclosed embodiments will be readily apparent to those skilled inthe art, and the general principles defined herein may be applied toother embodiments and applications without departing from the spirit andthe scope of the invention. Thus, the present invention is not intendedto be limited to the embodiments disclosed, but is to be accorded thewidest scope consistent with the principles and features disclosedherein.

As is noted above, the ideal waveform applied in FAIMS is a combinationof two sinusoidal waves of frequency ω and 2ω. The two waves are ofamplitudes that differ by a factor of two and are also offset by a phaseangle (Θ) of π/2 radians (equivalent to 90°), resulting in a waveformthat is defined by Equation 2, below:V(t)=A sin(ωt)+B sin(2ωt−Θ)  (2)where V(t) is the asymmetric waveform voltage as a function of time, Ais the amplitude of the first sinusoidal wave at frequency ω, where ω isthe waveform frequency in radians/sec, and B is the amplitude of thesecond sinusoidal wave at a frequency 2ω.

In a waveform having an optimum shape, A=2B, and Θ is equal to π/2. Theelectronic circuit must maintain these two conditions in order toachieve the waveform with the correct asymmetric waveform shape forstable performance of a FAIMS system attached thereto. Additionally, thepeak voltage on the highest voltage side of the asymmetric waveform(defined as DV above) must be maintained constant, and equal to A+B. Theelectronic circuit should therefore track, modify and control threeparameters to maintain the three desired relationships of the twocomponent sinusoidal waves and to obtain the desired waveform.

Referring to FIG. 1, shown is a plurality of cycles of an asymmetricwaveform that is formed as a combination of first and second sinusoidalwaves of frequency ω and 2ω, respectively. The correct asymmetricwaveform shape shown in FIG. 1 is established by collecting sample datapoints from the waveform, for example by analog-to-digital (A/D)sampling, in order to acquire a representative set of data points fromall portions of the asymmetric waveform. In other words, the A/D datapoints are taken randomly, at frequencies that are higher or lower thanthe waveform itself. However, it is necessary that this array of datapoints of the signal intensity of the asymmetric waveform correctlyrepresent all time periods within the waveform. For example, the sampledata points should include points near the peak voltage 2 in thepolarity of maximum voltage applied, as well as points near the twopeaks 4 of maximum voltage at the other polarity and in the dip 6between the two peaks 4. If the waveform is sampled across all times,the series of points thus acquired can be subjected to simple tests todetermine if the waveform shape is optimum.

By way of a non-limiting example, if a perfect sinusoidal wave (notshown) is sampled, the number of data points with positive measuredsignal equals the number of data points with negative measurements.Similarly the number of points at any given measurement value (signalvoltage) in the positive polarity equals those of the same absolutenegative voltage. These results are predicted because of the symmetry ofthe original sinusoidal wave.

A similar analysis is possible for the asymmetric waveform used inFAIMS. For example, the maximum signal voltage on one polarity must notequal the maximum measured signal of the opposite polarity. The maximummeasurement is expected to correspond to A+B as described above, and theopposite polarity maximum is expected to be (A+B)/2. Moreover, sincethere is one peak 2 in the first, maximum polarity side of the waveform,and two peaks 4 in the opposite polarity, the number of points at eachof these two values of signal measurement differ, while remaining higherin number than most other measurement values. However, because of theshape of the asymmetric waveform another measurement value will besignificant, and this is the value of the dip 6 between the two peaks onthe lower voltage side of the asymmetric waveform. Since the voltage istemporarily invariant in this valley, the number of data points withthis measurement value is anomalously high when compared to a sinusoidalwaveform, which lacks any significant numbers of data points other thanat the maxima. From the definition of the asymmetric waveform function,the measured signal in the dip 6 is expected to be A−B.

Referring again to FIG. 1, illustrated are several cycles of anasymmetric waveform that is formed according to Equation 2 above forA+B=1 and A/B=2. The peak values 2 of the waveform are therefore equalto A+B. The opposite polarity part of the waveform, negative polarity inthis example, is characterized by a dip 6 and two peak values 4. Asnoted above, the peak 2 in one polarity is A+B. The value at dip 6 isA−B (in this case A−B=⅓), and the peaks 4 in the opposite polarity areeach (A+B)/2 (in this case (A+B)/2=½).

Referring now to FIG. 2, shown is a distribution of the signal voltagefor the ideal waveform of FIG. 1. Data points are obtained bycalculating the signal voltage V(t) at a given time t using Equation 2.The data points are then sorted from most negative to most positivesignal value and are plotted sequentially as individual data pointsalong the horizontal axis. This provides a curve that is characteristicof the shape of the waveform. For simplicity, the total number of datapoints has been normalized to 100 percent. In other words, thehorizontal axis in FIG. 2 is the rank of the data points, expressed as apercent. If 1000 points are calculated and arranged in order ofmagnitude, then the smallest point is 0.1%, the 500th point is 50% andpoint 1000 is at 100% on the horizontal axis of FIG. 2.

Referring still to FIG. 2, about 62% of the data points are of negativepolarity and the remainder are positive. The polarity cross-over pointis labeled 8 in the figure. The maximum voltage of points in thepositive polarity is labeled at 10 and has a normalized magnitudenear 1. The most negative voltage data points are labeled at 12 on thefigure, and have a normalized voltage near −0.5. At point labeled 14 onthe figure, it is clear that a number of data points correspond toamplitude near 0.33, at about 50% of the data points as indicated by thelabels on the x-axis. These are the data points from the dip 6 in FIG.1.

The curves shown in FIG. 1 and FIG. 2 are illustrative of results thatare obtained for an ideal asymmetric waveform. Three specific types ofdeviation from the ideal asymmetric waveform are discussed in greaterdetail, as follows: first, a phase shift error; second an error in theratio of A/B (keeping A+B=1); and third, an error in the sum of A+B(keeping the ratio A/B=2). The electronics of a not illustratedasymmetric waveform generator may be used to identify such deviationsfrom the ideal waveform shape, and make adjustments to the driveelectronics accordingly.

Having regard to the first type of deviation, if the two sinusoidalwaves that are added together to create the asymmetric waveform shown inFIG. 1 are shifted in phase angle, then the two minima 4 in FIG. 1 willhave different values. In other words, one of the minima becomes morenegative whilst the other of the minima becomes less negative. If, forexample, a 5% error is imposed upon the phase angle, that is to say 5%of 90 degrees, then the values of the two minima 4 become quitedifferent. Under these experimental conditions of distorted waveform,the signal voltage of the data points of the most negative values becomemore negative than expected by about 4%. In other words, the data pointslabeled 12 in FIG. 2 change from a normalized signal voltage of about−0.5 to about −0.52 when the 5% phase angle error is imposed.

In the second type of deviation the ratio A/B varies while retaining thenormalized relationship A+B=1. The second type of deviation causes anerror in the value of the dip 6 shown on FIG. 1. For example, if A/B is1.9, and the data points from this distorted version of the asymmetricwaveform are arranged in order of ascending values, from negative topositive as was described with reference to FIG. 2, the signal voltageof the points that appear near a rank of 50% become less negative andcreate a relative error of about 6% compared to corresponding points forthe ideal waveform, which appear near label 14 in FIG. 2.

In the third type of deviation the ratio A/B=2 is constant but the sumA+B deviates from 1. A deviation of 2.4% in A+B, for example A+B=1.024,results in a 2.4% relative error compared to the ideal waveform for allof the points that are plotted in the manner that was described withreference to FIG. 2. For example, the points located near the maximumvoltage of points in the positive polarity shown at label 10 in FIG. 2increase from about 1.0 for the ideal waveform to about 1.024 when theerror is imposed.

Referring now to FIG. 3, shown are the relative error plots relating todifferences between the ideal asymmetric waveform of FIG. 1 anddifferent versions of the waveform, each different version of thewaveform distorted by one of the three specific types of deviationdescribed above.

Referring now to FIG. 4 a, the same data that is contained in FIG. 3 isreproduced along an expanded vertical scale for improved clarity. Asolid line 120 in FIG. 4 a denotes a relative error plot correspondingto a waveform with a phase shift error, which also is shown separatelyin FIG. 4 b. A dash-dot line 122 in FIG. 4 a denotes a relative error inthe relative amplitude of the component sinusoidal waves, which also isshown separately in FIG. 4 c. A dashed line 124 in FIG. 4 a denotes arelative error in the sum of the amplitudes of the component sinusoidalwaves, which also is shown separately in FIG. 4 d. The procedure forproducing such relative error plots is described in greater detail,below.

The first step in the procedure for producing the relative error plotsshown at FIGS. 4 a to 4 d is to collect a series of data points, i.e.,signal voltage magnitudes during the asymmetric waveform, whichrepresent all parts of the asymmetric waveform. For example, if 100 datapoints are collected rapidly in succession during one cycle of theasymmetric waveform, then this sampling of 100 points represents alltimes during the asymmetric waveform. If the data collection is uniformin time, then these 100 points are equally spaced over the duration ofthe asymmetric waveform. In a second step of processing the data, these100 points are arranged in order from smallest to largest, so as toproduce a plot similar to the one shown in FIG. 2. Next, each of the 100points, which was arranged from smallest to largest, is compared withthe points from an ideal asymmetric waveform. The points for an idealasymmetric waveform are calculated by entering appropriate values oftime t in Equation 2 as described above. The relative error iscalculated as:

$\begin{matrix}\frac{( {{ideal}\mspace{14mu}{waveform}\mspace{14mu}{signal}\mspace{14mu}{voltage}} ) - ( {{actual}\mspace{14mu}{waveform}\mspace{14mu}{signal}\mspace{14mu}{voltage}} )}{( {{ideal}\mspace{14mu}{waveform}\mspace{14mu}{signal}\mspace{14mu}{voltage}} )} & (3)\end{matrix}$A plot of the relative error difference i.e. normalized to the magnitudeat that point is prepared as shown at FIG. 3 and FIGS. 4 a to 4 d. Ifthe new data set represents a perfectly formed asymmetric waveform, thenall data points are zero.

If the waveform being analyzed is generated with some error, for examplea 5% error in the phase shift of the higher frequency sinusoidal wave,then the resulting asymmetric waveform is not shaped ideally. Although aplot of the distribution of signal voltage may look very much like FIG.2 when arranged from most negative to most positive in magnitude, infact there are significant differences in the shape of the actualwaveform when compared to the ideal waveform. These differences are moreapparent when the relative error is plotted as shown at FIG. 3 and FIG.4 b.

For example, the 5% shift in phase angle results in a relative errorplot that is shown in FIG. 3 and FIG. 4 a at solid line 120 and at FIG.4 b. Since the data points are arranged from left to right in order ofincreasing magnitude of signal voltage, the data points of most negativepolarity (in this example) appear near the label 20 in FIG. 4 b and areapproximately 4% lower than equivalent points in the case of the idealasymmetric waveform. Accordingly, the phase angle shift has caused oneof the minima 4 shown at FIG. 1 to become approximately 4% more negativethat is expected in the ideal waveform. Although elsewhere on the plot,especially in the region shown by label 26, the relative errors can bevery large, this large relative error is not as useful because theabsolute values of the amplitudes of the data points are close to zero.In particular, the signal voltage changes from negative to positive atthe polarity cross-over point 8 along the horizontal x-axis of FIG. 2and is small in magnitude in this vicinity.

The second type of error, a 5% error in the ratio A/B, is shown asdash-dot line 122 in FIG. 3 and FIG. 4 a. In the region near the label22 in FIG. 4 c it is seen that the relative error in the magnitude ofthe signal voltage from the distorted waveform differ from those of theideal waveform by more than 3%. This region corresponds to data pointslabeled at 14 in FIG. 2, which are expected to be approximately constantand about ⅓ of the amplitude of the maximum in the opposite polarity.The data points labeled at 14 in FIG. 2 are indicative of the dip region6 of FIG. 1.

The easiest type of error to observe is the third, in which the sum A+Bis wrong, for example, by about 2.4%. The net result of this distortionis a relative error of 2.4% at every point throughout the cycle of thewaveform. This is shown in FIG. 3, and in FIG. 4 a as a dashed line 124,and in FIG. 4 d.

Accordingly, the magnitude of each one of the three types of deviationfrom the ideal waveform is determined. The information relating to eachone of the three types of deviation is used in a feedback and controlsystem for optimizing the asymmetric waveform generator LC tuningelectronics, in order to achieve an asymmetric waveform with the correctshape for stable performance of the FAIMS system attached thereto. Thewaveform parameters are:

-   -   (a) dispersion voltage (DV)=A+B    -   (b) A=2B    -   (c) phase angle, Θ=π/2        The electronics of the waveform generator maintains these three        relationships.

Referring now to FIG. 5, shown is a simplified flow diagram of a methodof optimizing asymmetric waveform generator LC tuning electronicsaccording to an embodiment of the instant invention. At step 100 agenerated asymmetric waveform is sampled to obtain a set of data points.For example, step 100 is performed as a fast analog-to-digital (A/D)sampling of the signal voltage to collect 100 data points within onecycle of the waveform. A plot of the magnitude, or A/D values, of thesedata points as a function of time of collection yields a trace thatresembles an oscilloscope trace of the original generated asymmetricwaveform. Alternatively, the set of data points is obtained as a slow,random, sampling version of A/D, which eventually collects sample datapoints from every portion of the generated asymmetric waveform. Forexample, the A/D collection of 100 data points randomly, one new datapoint each millisecond, results in the acquisition of the 100 datapoints in approximately 100 milliseconds. Since the asymmetric waveformis repeating rapidly, perhaps in the megahertz range, no two of theseA/D data points is sampled from the same cycle of the waveform. However,each data point is sampled from somewhere during the cycle of thewaveform. Similarly, each one of the following ninety-nine data pointsis sampled from a random point in a widely separated (in time) cycle ofthe waveform from the previous sampling. If the data points are actuallyrandom, then every region of the generated asymmetric waveform, giventhe finite number of data points collected, is sampled although one doesnot know from which time in the period of the generated asymmetricwaveform each data point is acquired. One cannot reconstruct theequivalent of an oscilloscope trace of the original waveform shapebecause the “time” values of the data points relative to the originalwaveform is unknown, hence the randomness of this sampling method.

At step 102, the set of data points are arranged by order of magnitude,such as for example from most negative to most positive. If the datapoints are collected randomly from all parts of the waveform at step100, then the distribution resembles that shown in FIG. 2 when plotted.Of course, generating a plot similar to the one shown in FIG. 2 is notan essential feature of the instant invention.

At step 104, the data points arranged by order of magnitude are comparedto template data relating to a desired asymmetric waveform, for instancean ideal waveform. Preferably, three comparisons are performed at step104: a first comparison for data points close to 100% along thehorizontal axis of FIG. 4 a to look for an error in A+B where A/B=2; asecond comparison for data points close to 0% along the horizontal axisof FIG. 4 a to look for an error in phase angle; and a third comparisonfor data points close to 45–50% along the horizontal axis of FIG. 4 a tolook for an error in A/B where A+B is equal to the DV.

When the result of the first comparison is indicative of a deviationfrom ideal shape, it is suggestive that the amplitude of the asymmetricwaveform should be corrected. Having regard to the specific exampleshown at FIG. 4 d, the amplitude of the asymmetric waveform should bedecreased because the sum of A+B is too large, i.e. the trace must bemoved “upwards” to zero. In particular, at step 104 a negative relativeerror of approximately 2.4% is determined in the data points near 100%along the horizontal axis. Since the relative error at any given pointis determined according to [(ideal waveform voltage)−(actual waveformvoltage)]/(ideal waveform voltage), a negative relative error indicatesthat the actual waveform voltage exceeds the ideal waveform voltage.Advantageously, the other types of distortion do not cause a significantrelative error in the data points near 100% along the horizontal axis.Accordingly, at step 106 a correction is determined for adjusting thesum of A+B to be equal to the DV.

After the sum A+B is set equal to the DV, the second comparison isperformed. When the result of the second comparison is indicative ofdeviation from ideal shape, then the waveform suffers not fromdistortion in the magnitude of A+B, but rather from a phase shift error.A correction of the phase angle is therefore determined at step 106.This correction may be performed in an iterative manner, until thedeviation is reduced to zero. Clearly, the relative error that isdetermined in the data points near 0% along the horizontal axis can alsohave a contribution from the A+B function. In particular, the dashedline 124 extends from 0% to 100% in FIG. 4 a with a constant relativeerror value of −2.4%. Accordingly, the sum A+B should be set to thecorrect value prior to attempting to adjust the phase angle, and the sumA+B should be revised repeatedly during the phase angle adjustment.

When the result of the third comparison is indicative of deviation fromideal shape, and when the A+B function error is close to zero, then adistortion may arise as a result of an error in the magnitude of A/B;This type of deviation is indicated by non-zero relative errors in the45–50% range of data points. In this case, a correction of the A/Bfunction is determined at step 106.

Referring now to FIG. 6, shown is a simplified flow diagram of a methodof optimizing asymmetric waveform generator LC tuning electronicsaccording to another embodiment of the instant invention. At step 110, aset of data points is obtained that is indicative of the generatedasymmetric waveform. For example, the generated asymmetric waveform issampled as described with reference to FIG. 5, or the set of data pointsis obtained in a different way. Once obtained, the set of data pointsare arranged by order of magnitude, such as for example from smallest tolargest, at step 112. At step 114, the data points arranged by order ofmagnitude are compared to template data relating to a desired asymmetricwaveform, for instance an ideal waveform. Preferably, three comparisonsare performed at step 114: a first comparison for data points close to100% along the horizontal axis of FIG. 4; a second comparison for datapoints close to 0% along the horizontal axis of FIG. 4; and a thirdcomparison for data points close to 45–50% along the horizontal axis ofFIG. 4. In dependence upon the comparison at step 114, an adjustment ismade at step 116 to at least one of a phase angle difference between thetwo sinusoidal waves and an amplitude of at least one of the twosinusoidal waves.

These calculations, described for example with reference to FIGS. 5 and6, are readily implemented in control software of the waveformgenerator. The type of error is determined and appropriate correctiveactions are taken. Correction of the phase angle or the correction ofthe ratio A/B can be performed in either order, but the A+B functionmust be set first to the correct value. Referring again to FIG. 4, asmall error in the phase angle has minimum contribution to the relativeerror at the 45–50% region of FIG. 4. Similarly, small shifts of A/Bcontribute small relative errors in the 0–5% region of FIG. 4.

Referring now to FIG. 7, shown is a simplified flow diagram of a methodof adjusting the different waveform parameters arising from minorfluctuations during operation. The method of FIG. 7 is implemented, forexample, subsequent to step 106 of FIG. 5 or during step 116 of FIG. 6.At decision step 130 it is determined whether the sum A+B is equal toDV. If no, as shown in FIG. 8 at label 24, then at step 132 the sum A+Bis adjusted. For example, if A+B is too large, the amplitudes of bothsinusoidal waves that are used to form the waveform are decreased. Thisreturns the sum A+B to the correct value as shown by the relative errorof 0% at 100% rank of data points in FIG. 9. At decision step 134, it isdetermined whether the phase angle error is minimized. If no, then atstep 136 one sinusoidal wave is shifted relative to the other. Theshifts are applied until the relative error at label 20 in FIG. 9approaches zero. Preferably, the sum A+B is also adjusted as necessary,such that A+B continues to equal the DV. At decision step 138 it isdetermined whether the error in the ratio of A/B is minimized. If no,then at step 140 the amplitude of one of the sinusoidal waves isincreased while the amplitude of the second sinusoidal wave isdecreased, for example. The corrections are applied until the relativeerror at label 22 in FIG. 9 determined at decision step 138 decreases toa minimum value, but not necessarily to zero. Preferably, the sum A+B isalso adjusted as necessary, such that A+B continues to equal the DV.Once it is determined that the errors in both the phase angle and theamplitudes of the sinusoidal waves are within predetermined thresholdvalues, tuning is complete. At step 142 a predetermined interval of timeis allowed to lapse before returning to step 130 to check the waveformfor errors. Advantageously, the generated asymmetric waveform isoptimized and maintained in its ideal form by a cyclic process ofrepeating these tests and adjusting the amplitudes and phases of thesinusoidal waves used to produce the asymmetric waveform.

Referring now to FIG. 10, shown is a simplified flow diagram of anothermethod of adjusting the different waveform parameters. According to thisalternative method, the ratio of A/B is corrected before the phase angleis corrected. The method of FIG. 10 is implemented, for example,subsequent to step 106 of FIG. 5 or during step 116 of FIG. 6. Atdecision step 130 it is determined whether the sum A+B is equal to DV.If no, then at step 132 the sum A+B is adjusted. For example, if A+B istoo large, the amplitudes of both sinusoidal waves that are used to formthe waveform are decreased. This returns the A+B to the correct value.At decision step 138, it is determined whether the relative error in theratio of A/B is minimized. If no, then at step 140 the amplitude of oneof the sinusoidal waves is increased while the amplitude of the secondsinusoidal wave is decreased, for example. The corrections are applieduntil it is determined at decision step 138 that the relative error inthe ratio of A/B is a minimum value, but not necessarily zero.Preferably, the sum A+B is also adjusted as necessary, such that A+Bcontinues to equal the DV. Finally, at decision step 134 it isdetermined whether the phase angle error is minimized. If no, then onesinusoidal wave is shifted relative to the other at step 136. The shiftsare applied until the relative error at label 20 in FIG. 9 approacheszero. Preferably, the sum A+B is also adjusted as necessary, such thatA+B continues to equal the DV. When it is determined that the relativeerrors in both the ratio A/B and the phase angle are withinpredetermined threshold values, tuning is complete and at step 142 apredetermined interval of time is allowed to lapse before returning tostep 130 to check for fluctuations in the waveform. Advantageously, thegenerated asymmetric waveform is optimized and maintained in its idealform by a cyclic process of repeating these tests and adjusting smallerrors in the amplitudes and phases of the sinusoidal waves occurringdue to, for instance, random environmental fluctuations.

Numerous other embodiments may be envisaged without departing from thespirit and scope of the instant invention.

1. A method of controlling an asymmetric waveform generated by anasymmetric waveform generator as a combination of two sinusoidal waveshaving respective frequencies that differ from each other by a factor oftwo, the method comprising the steps of: sampling the generatedasymmetric waveform to obtain a set of data points that is indicative ofthe generated asymmetric waveform; arranging the sampled data points inan order according to magnitude; comparing the arranged sampled datapoints to template data relating to a desired asymmetric waveform; independence upon the comparison, determining a correction to thegenerated asymmetric waveform, the determined correction for adjustingat least one of a phase angle difference between the two sinusoidalwaves and an amplitude of at least one of the two sinusoidal waves; and,adjusting LC tuning electronics of the asymmetric waveform generator independence upon the determined correction, so as to control theasymmetric waveform being generated thereby.
 2. A method according toclaim 1, wherein the generated asymmetric waveform has the general formV(t)=A sin (ωt)+B sin (2ωt−Θ), where V(t) is the asymmetric waveformvoltage as a function of time, A is the amplitude of the first sine waveat frequency ω, where ω is the frequency in radians/sec, B is theamplitude of the second sine wave at a frequency 2ω, and Θ is a phaseangle offset between the first sinusoidal wave and the second sinusoidalwave.
 3. A method according to claim 2, wherein the determinedcorrection is for satisfying the condition A+B is equal to a desiredasymmetric waveform peak voltage.
 4. A method according to claim 3,wherein the determined correction is for satisfying the condition Θ=π/2.5. A method according to claim 4, wherein the determined correction isfor satisfying the condition that A/B equals a predetermined value.
 6. Amethod according to claim 3, wherein the determined correction is forsatisfying the condition that A/B equals a predetermined value.
 7. Amethod according to claim 2, wherein the determined correction is forsatisfying the condition Θ=π/2.
 8. A method according to claim 2,wherein the determined correction is for satisfying the condition thatA/B equals a predetermined value.
 9. A method according to claim 2,including the step of repeating the steps of claim 1 in an iterativefashion.
 10. A method according to claim 1, comprising a step ofobtaining the template data, the template data including a set of datapoints relating to the desired asymmetric waveform.
 11. A methodaccording to claim 10, wherein the step of comparing comprises a step ofdetermining a difference between each arranged sampled data point and acorresponding data point of the template data.
 12. A method according toclaim 10, wherein the step of obtaining template data comprises the stepof retrieving template data from a memory.
 13. A method according toclaim 10, wherein the step of obtaining template data comprises the stepof evaluating V(t)=A sin(ωt)+B sin (2ωt−Θ) for each one of a pluralityof t-values, for determining a first set of data points, and furthercomprises the step of arranging the first set of data points in an orderaccording to magnitude.
 14. A method according to claim 10, wherein theset of data points that is indicative of the generated asymmetricwaveform and the template data relating to the desired asymmetricwaveform include a same number of data points.
 15. A method according toclaim 1, wherein the step of sampling is performed as ananalog-to-digital sampling for collecting data points contained withinone cycle of the generated asymmetric waveform.
 16. A method accordingto claim 1, wherein the step of sampling is performed as ananalog-to-digital sampling, for collecting data points from a pluralityof portions of the generated asymmetric waveform during a period of timeoverlapping with a plurality of different cycles of the generatedasymmetric waveform.
 17. A method according to claim 1, including thestep of repeating the steps of claim 1 in an iterative fashion.
 18. Astorage medium encoded with machine-readable computer program code forcontrolling an asymmetric waveform generated by an asymmetric waveformgenerator as a combination of two sinusoidal waves having respectivefrequencies that differ from each other by a factor of two, the storagemedium including instructions for: obtaining a set of data points thatis indicative of the generated asymmetric waveform; arranging the datapoints in an order according to magnitude; obtaining template dataincluding a set of data points relating to a desired asymmetricwaveform; comparing values of data points within a predetermined rangeof the arranged data points to values of data points within acorresponding predetermined range of the template data; in dependenceupon the comparison, determining a correction to the generatedasymmetric waveform, the determined correction for adjusting at leastone of a phase angle difference between the two sinusoidal waves and anamplitude of at least one of the two sinusoidal waves; and, adjusting LCtuning electronics of the asymmetric waveform generator in dependenceupon the determined correction, so as to control at least one of thephase angle difference between the two sinusoidal waves and theamplitude of at least one of the two sinusoidal waves.